Related papers: Optical Flow on Moving Manifolds
We tackle the problem of estimating optical flow from a monocular camera in the context of autonomous driving. We build on the observation that the scene is typically composed of a static background, as well as a relatively small number of…
The accuracy of learning-based optical flow estimation models heavily relies on the realism of the training datasets. Current approaches for generating such datasets either employ synthetic data or generate images with limited realism.…
Many problems in machine learning can be formulated as solving entropy-regularized optimal transport on the space of probability measures. The canonical approach involves the Sinkhorn iterates, renowned for their rich mathematical…
Flow-based methods have demonstrated promising results in addressing the ill-posed nature of super-resolution (SR) by learning the distribution of high-resolution (HR) images with the normalizing flow. However, these methods can only…
Following work of Ecker, we consider a weighted Gibbons-Hawking-York functional on a Riemannian manifold-with-boundary. We compute its variational properties and its time derivative under Perelman's modified Ricci flow. The answer has a…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of…
The nonlinear wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$ determines a flow of conservative solutions taking values in the space $H^1(\mathbb{R})$. However, this flow is not continuous w.r.t. the natural $H^1$ distance. Aim of this paper is to…
Finding image correspondences remains a challenging problem in the presence of intra-class variations and large changes in scene layout.~Semantic flow methods are designed to handle images depicting different instances of the same object or…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
Semantic segmentation and semantic image synthesis are two representative tasks in visual perception and generation. While existing methods consider them as two distinct tasks, we propose a unified framework (SemFlow) and model them as a…
The main objective of this article is to study the mean curvature flow into an ambient compact smooth manifold M with boundary and with a Riemannian metric that evolves by a self-similar solution of the Ricci flow coupled with the harmonic…
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then…
Obtained by moving object detection, the foreground mask result is unshaped and can not be directly used in most subsequent processes. In this paper, we focus on this problem and address it by constructing an optical flow based moving…
Large displacement optical flow is an integral part of many computer vision tasks. Variational optical flow techniques based on a coarse-to-fine scheme interpolate sparse matches and locally optimize an energy model conditioned on colour,…
Over three decades ago the advection-diffusion equation for a steady fluid velocity field was homogenized, leading to a Stieltjes integral representation for the effective diffusivity, which is given in terms of a spectral measure of a…
Occlusions pose a significant challenge to optical flow algorithms that rely on local evidences. We consider an occluded point to be one that is imaged in the first frame but not in the next, a slight overloading of the standard definition…
In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness alternatives for the flow, giving a lower bound on the maximal…
Scene flow prediction is a crucial underlying task in understanding dynamic scenes as it offers fundamental motion information. However, contemporary scene flow methods encounter three major challenges. Firstly, flow estimation solely based…
Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally…